On an exotic topology of the integers
General Topology
2010-08-05 v1 Number Theory
Abstract
We study some interesting properties of Furstenberg's topology of the integers. We show that it is metrizable, totally disconnected, and (Z,+,.) is a topological ring with respect to this topology. As an application, we show that any two disjoint sets of primes can be separated by arithmetic progressions.
Keywords
Cite
@article{arxiv.1008.0713,
title = {On an exotic topology of the integers},
author = {Rezsö L. Lovas and István Mezö},
journal= {arXiv preprint arXiv:1008.0713},
year = {2010}
}
Comments
6 pages